1. Field of the Invention
The present invention relates to a method and an apparatus for transmitting a sparse signal, and a method and an apparatus for recovering the sparse signal via a belief propagation and a Bayesian hypothesis test (BHT).
2. Description of the Related Art
When a signal length of a sparse signal is N, the sparse signal includes K (N>>K) non-zero elements and (N−K) zero elements. A compressed sensing scheme is a signal compressing and processing scheme capable of significantly reducing an amount of information of the sparse signal.
A transmitter generates a measurement signal y obtained by compressing and sensing a target sparse signal x by using a sensing matrix Φ and transmits the measurement signal y. A receiver finds the target sparse signal x having the minimum non-zero elements among infinite solutions satisfying y=Φx. A method for recovering such a sparse signal is simply expressed as shown in following equation. However, according to the method for recovering the sparse signal, since xCK search operations are required in order to recover the target signal x, complexity is exponentially increased if the values of N and K are increased.
                                                        min                              x                _                                      ⁢                                                                                                  x                    _                                                                    0                            ⁢                                                          ⁢                              s                .                t                .                                                                  ⁢                                  y                  _                                                              =                                    Φ              ⁢                                                          ⁢                              x                _                                      -                          [                              P                ⁢                                                                  ⁢                0                            ]                                      ⁢                                  ⁢                                                        x              _                                            0                =                  {                      #            ⁢                                                  ⁢            of            ⁢                                                  ⁢            non            ⁢                          -                        ⁢            zero            ⁢                                                  ⁢            elements            ⁢                                                  ⁢            of            ⁢                                                  ⁢                          x              _                                }                            Equation      
In addition, as schemes for recovering compressed measurement signals, an OMP (Orthogonal Matching Pursuit) scheme, an StOMP (Stagewise Orthogonal Matching Pursuit) scheme, and a chain pursuit scheme have been used. However, the above schemes represent a low recovery success rate, or are applicable to very sparse signals.